How to solve a 4x4 Rubik's cube by reduction
The usual way to solve a 4x4 Rubik's cube is the reduction method: you turn it into something that behaves like a 3x3, then solve it with a 3x3 method. A 4x4 has 8 corners, 24 edge pieces (two on each edge, often called wings) and 24 center pieces (four on each face). Reduction has three stages: build the six centers, pair the 24 edge pieces into 12 edges, then solve the cube like a 3x3 with outer turns. Two cases cannot happen on a 3x3, so they get their own algorithms: OLL parity and PLL parity.
4x4 notation. R turns only the outer right layer. Rw turns the right face and the layer next to it together. 2R turns only that second layer. Uw, Fw, 2L and so on work the same way, always clockwise as you look at that face; x turns the whole cube like R. The tool above plays any sequence you type.
1. Centers
A 4x4 has no fixed centers, so you choose: build white and yellow on opposite faces first, then the four side centers in the order of a solved cube (with white on top and green in front, red goes on the right). Each center is a 2x2 block. Make pairs of two matching center pieces, then bring a pair into its face with a wide turn, a turn of the top, and the wide turn back: that out, turn, back pattern moves pieces in without breaking centers you already built. The example plays the moves the 4x4 solver found for this stage on a scrambled cube; they are shorter than what a person would do, but the goal is the same.
2. Pair the edges
Each edge of the reduced cube is two edge pieces with the same two colors. To pair two of them, put one on the front-left edge in the upper row and its partner on the front-right edge in the lower row. Uw' turns the top two layers and joins them at the front-right. R U R' lifts the new pair into the top layer and brings the edge from the top back down to the front-right in its place, and Uw puts the centers back.
Uw' R U R' UwJoin, lift out, turn back. The centers end where they started.
In the top layer the new pair is safe, because a turn of the top two layers moves it as one piece. R U R' touches none of the other three middle-layer edges, so keep finished pairs there or in the bottom layer, and keep an unpaired edge at the top back so you never bring a finished pair down. Repeat until every edge is paired; the last two take some juggling with the same moves.
3. Solve it like a 3x3
Now solve the cube with any 3x3 method, for example our beginner method, using only outer turns (R, U, F and so on) so the centers and edge pairs stay together. Treat each center block as a 3x3 center and each edge pair as one 3x3 edge. In this example the solver first fixed PLL parity, which it can see coming, then solved the rest as a 3x3.
OLL parity: one edge flipped
On the last layer you may find an odd number of flipped edges, for example a single edge with yellow facing the side. That never happens on a 3x3; on a 4x4 it is OLL parity. Hold the flipped edge at the front of the top face and do:
2R2 B2 U2 2L U2 2R' U2 2R U2 F2 2R F2 2L' B2 2R2Flips the front top edge. Nothing else changes.
Another common sequence is this one. It also flips the front top edge, but it moves other pieces of the top layer too (the two front top corners trade places, and so do the left and right top edges), so continue the last layer from there:
Rw U2 x Rw U2 Rw U2 Rw' U2 Lw U2 Rw' U2 Rw U2 Rw' U2 Rw'Flips the front top edge and rearranges the rest of the top layer. The bottom three layers stay solved.
PLL parity: two edges swapped
At the very end you may find two edges swapped, or a last-layer case that no 3x3 algorithm fixes. That is PLL parity. Hold two top edges that need to swap at the front and the back, and do:
2R2 U2 2R2 Uw2 2R2 Uw2 U2Swaps the front and back top edges. Nothing else changes.
Many guides write it without the final U2; then the top layer ends a half turn off. If the two edges that need to swap sit side by side, do the algorithm with any two opposite top edges at the front and the back, then finish with a 3x3 last-layer algorithm.
How the examples were checked
Every algorithm on this page was replayed on a cube model in a test: the two parity algorithms change exactly the stickers described here and nothing else, the edge pairing sequence returns every center and leaves the new pair in the top layer, and each example stage reaches its goal (all centers built, all edges paired, cube solved). To solve your own 4x4 move by move, use the 4x4 solver.
The 5x5 guide uses the same reduction idea with one more ring of center pieces and three-piece edges.
Solver tested . Found a problem? Tell us.
Questions
What is parity on a 4x4 Rubik's cube?
A position the 3x3 stage cannot fix because the edge pieces were paired in an arrangement no 3x3 can have: one flipped edge (OLL parity) or two swapped edges (PLL parity). Each has its own algorithm on this page.
How do I know which color center goes where on a 4x4?
Build white and yellow on opposite faces, then hold white on top: green goes in front, red on the right, blue at the back and orange on the left, as on a solved cube. If two side centers end up swapped, the cube cannot be solved as a 3x3 later.
Can I use my 3x3 method on a 4x4?
Yes, once the centers are built and the edges paired. Use only outer turns during the 3x3 stage, and learn the two parity algorithms for the cases a 3x3 never shows.
What does 2R mean, and how is it different from Rw?
2R turns only the second layer from the right. Rw turns the outer right layer and the second layer together. The parity algorithms use 2R so that the outer layer does not move.
Is reduction the only way to solve a 4x4?
No. Other methods exist, for example Yau, which builds some edges before the last centers, and the cage method, which solves edges and corners before the centers. Reduction is the one most guides teach first because it reuses a 3x3 method.